Plastic deformation history, effect

It is instructive to describe elastic-plastic responses in terms of idealized behaviors. Generally, elastic-deformation models describe the solid as either linearly or nonlinearly elastic. The plastic deformation material models describe rate-independent behaviors in terms of either ideal plasticity, strainhardening plasticity, strain-softening plasticity, or as stress-history dependent, e.g. the Bauschinger effect [64J01, 91S01]. Rate-dependent descriptions are more physically realistic and are the basis for viscoplastic models. The degree of flexibility afforded elastic-plastic model development has typically led to descriptions of materials response that contain more adjustable parameters than can be independently verified. 

In structural design, it is important to distinguish between various modes in the product. The behavior of any material in tension, for example, is different from its behavior in shear, as with plastics, metals, concrete, etc. For viscoelastic materials such as plastics, the history of deformation also has an effect on the response of the material, since viscoelastic materials have time- and temperature-dependent material properties. 

Unified Plasticity Model The time-independent plastic deformation and fee time-dependent creep deformation arise from fee same fundamental mechanism of dislocation motion. Hence, a constitutive model which captures both of these deformation mechanisms is desirable. Such a constitutive model is referred to as a unified plasticity model. A commonly-used unified plasticity model is the Anand s model. This is a rate-dependent phenomenological model (Ref 17 and 18). There are two basic characteristics of fee Anand s model. First, no explicit yield criterion is specified, and second, a single internal state variable (ISV) s, the deformation resistance, represents the isotropic resistance to inelastic strain hardening. Anand s model can represent fee strain rate and temperature sensitivity, strain rate history effects, strain hardening, and fee restoration process of dynamic recovery. Equation 9 shows the functional form of fee flow equation that accommodates fee strain rate dependence on the stress ... 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

As we have emphasized aheady, the study of plasticity is one of the centerpieces of the mechanics of materials. A wide array of technologies depend upon the ability to deform materials into particular desirable shapes, while from a scientific perspective I personally find the subject of great interest because it is an intrinsically dissipative process featuring history dependence and is a strong function of the material s microstructure. In addition, from the effective theory perspective, the study of plasticity is built around the motion and entanglement of dislocations which requires the construction of theories of lines and their interaction thus ushering in a certain nonlocality to the phenomenon right from the outset. 

If this deformation field does not fulfill the geometrical compatibility, a strain tensor related to stress is generated. The constitutive equation, which represents the mechanical behavior of the material, relates this strain tensor and the stress tensor. Due to the memory effect of wood, this tensor has to be divided into two parts (1) an elastic strain, connected to the actual stress tensor and (2) a memory strain, which includes all the strain due to the history of that point (e can deal with plasticity, creep, mechanosorption, etc.). 

Compaction, consolidation, and subsidence. A formal approach to modeling compaction, consolidation, and subsidence requires the use of well-defined constitutive equations that describe both fluid and solid phases of matter. At the same time, these would be applied to a general Lagrangian dynamical formulation written to host the deforming meshes, whose exact time histories must be determined as part of the overall solution. These nonlinear deformations are often plastic in nature, and not elastic, as in linear analyses usually employed in structural mechanics. This finite deformation approach, usually adopted in more rigorous academic researches into compressible porous media, is well known in soil mechanics and civil engineering. However, it is computationally intensive and not practical for routine use. This is particularly true when order-of-magnitude effects and qualitative trends only are examined. 

Polymers are viscoelastic materials in which deformations that are caused by an external force are time-dependent. Hence, the shape of the material is influenced by the previous mechanical history and it exhibits the memory phenomenon [1]. A typical shape memory aspect of polymeric materials is that of rubber elasticity. A rubber returns to its original shape even after terrific deformation. On the other hand, plastics return to their original shape slowly after they have been stretched or bent. There are fibers or stretched films that shrink suddenly at a certain temperature. In a broad sense, polymeric materials more or less possess shape memory effects. It is possible to enhance the memory further and... 

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